When using the iOS ReplayKit to broadcast video feed, auto-rotation doesn't work

To repro:
1: Open attached project
2: Build for iOS
3: Adding following to Xcode info.plist:

<key>NSCameraUsageDescription</key>
<string>Front-facing camera during gameplay</string>
<key>NSMicrophoneUsageDescription</key>
<string>Record microphone for commentary</string>

4: Run on iOS 10 iPad (tested iPad pro iOS 10.1) with Mobcrush app installed
5: Accept permissions for camera and microphone
6: Click Start Broadcast button
7: Broadcast to Mobcrush
8: Rotate the device and see that the screen doesn't auto-rotate
9: Open "empty" Xcode project, start broadcasting and see that auto-rotation works